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12th Business Maths Weekly Test - 2 ( Applied Statistics )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( Applied Statistics )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Most commonly used index number is:

Volume index number
Value index number
Price index number
Simple index number

Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

110
108
100
109

Cost of living at two different cities can be compared with the help of

Consumer price index
Value index
Volume index
Un-weighted index

The upper control limit for \(\overset {-}{X}\) chart is given by

\(\bar { X } +{ A }_{ 2 }\bar { R } \)
\(\overset { = }{ X } +{ A }_{ 2 }R\)
\(\overset { = }{ X } +{ A }_{ 2 }\bar { R } \)
\(\overset { = }{ X } +{ A }_{ 2 }\overset { = }{ R } \)

A typical control charts consists of

CL, UCL
CL, LCL
CL, LCL, UCL
UCL, LCL

How many causes of variation will affect the quality of a product?

4
3
2
1

Variations due to natural disorder is known as

random cause
non-random cause
human cause
all of them

The value of ‘b’ in the trend line y=a+bx is

Always positive
Always negative
Either positive or negative
Zero

The quantities that can be numerically measured can be plotted on a

p - chart
c – chart
x bar chart
np – chart

The LCL for R chart is given by

\({ D }_{ 2 }\bar { R } \)
\({ D }_{ 2 }\overset { = }{ R } \)
\({ D }_{ 3 }\overset { = }{ R } \)
\({ D }_{ 3 }\bar { R } \)

The additive model of the time series with the components T, S, C and I is

y=T+S+C×I
y=T+S×C×I
y=T+S+C+I
y=T+S×C+I

While computing a weighted index, the current period quantities are used in the:

Laspeyre’s method
Paasche’s method
Marshall Edgeworth method
Fisher’s ideal method

Least square method of fitting a trend is

Most exact
Least exact
Full of subjectivity
Mathematically unsolved

The components of a time series which is attached to short term fluctuation is

Secular trend
Seasonal variations
Cyclic variation
Irregular variation

The assignable causes can occur due to

poor raw materials
unskilled labour
faulty machines
all of them

Part - B

Generic 5 - Answer All Question

Construct the cost of living index number for 2011 on the basis of 2007 from the given data using family budget method.

Commodities Price Weights

2007 2011

A 350 400 40

B 175 250 35

C 100 115 15

D 75 105 20

E 60 80 25

Calculate the cost of living index number for the following data.

Commodities Quantity
2005 Price

2005 2010

A 10 7 9

B 12 6 8

C 17 10 15

D 19 14 16

E 15 12 17

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities Price Quandity

2000 2010 2000 2010

Rice 38 35 6 7

Wheat 12 18 7 10

Rent 10 15 10 15

Fuel 25 30 12 16

Miscellaneous 30 33 8 10

Calculate Fisher’s price index number and show that it satisfies both Time Reversal Test and Factor Reversal Test for data given below.

Commodities Base Year Current Year

Price Quantity Price Quantity

Rice 150 5 11 6

Wheat 12 6 13 4

Rent 14 8 15 7

Fuel 16 9 17 8

Transport 18 7 19 5

Miscellaneous 20 4 21 3

Construct Fisher’s price index number and prove that it satisfies both Time Reversal Test and Factor Reversal Test for data following data.

Commodities Base Year Current Year

Price Quantity Price Quantity

Rice 40 5 48 4

Wheat 45 2 42 3

Rent 90 4 95 6

Fuel 85 3 80 2

Transport 50 5 65 8

Miscellaneous 65 1 72 3

Calculate Fisher’s price index number and show that it satisfies both Time Reversal Test and Factor Reversal Test for data given below.

Commodities Price Quandity

2003 2009 2003 2009

Rice 10 13 4 6

Wheat 125 18 7 8

Rent 25 29 5 9

Fuel 2511 14 8 10

Miscellaneous 14 17 6 7

Calculate the cost of living index number by consumer price index number for the year 2016 with respect to base year 2011 of the following data.

Commodities Price Quantity

Base year Current year

Rice 32 48 25

Sugar 25 42 10

Oil 54 85 6

Coffe 250 460 1

Tea 175 275 2

Calculate the cost of living index number for the year 2015 with respect to base year 2010 of the following data.

Commodities Number of
Units
(2010) Price
(2010) Price
(2015)

Rice 5 1500 1750

Sugar 3.5 1100 1200

Pulses 3 800 950

Cloth 2 1200 1550

Ghee 0.75 550 700

Rent 12 2500 3000

Fuel 8 750 600

Misc 110 3200 3500

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